Does the Market Adopt Sraffa's 'Self-replacing' Prices?

Piero Sraffa’s model of production for subsistence concerns the existence of unique exchange ratios which allow production to be repeated over time. In this paper we investigate the question whether a competitive market adopts these exchange ratios – a question Sraffa alluded to, but did not answer in his book. To this end we restrict our attention to the simple two-commodity case and «translate» Sraffa’s model in terms of the Edgeworth box diagram. When outputs are given and only one method of production is known in each industry, it is very easy to show that nothing prevents the market from adopting the «self-replacing» relative price. The introduction of a variety of methods makes things more complex and requires, special cases aside, to consider the outputs as variables to be determined within the model. It is shown that, with constant returns to scale and smooth isoquants in the two industries, the market does indeed adopt Sraffa’s self-replacing price.